CSCE 4115/5400 EXAM #2 SAMPLE QUESTIONS SOLUTION
1. A context-free grammar where every production is either of the form A BC or A a is
said to be in Chomsky Normal Form.
2. True or False. The class of languages accepted by nondeterministic Turing machines
CSCE 4115/5400 ASSIGNMENT #5 SOLUTION
1. Prove that the following are not context-free languages.
(a) L = cfw_w#wR #w | w cfw_0, 1 . Example strings in L include 01#10#01, 110#011#110,
and 000#000#000.
Let z = 0n #0n #0n . z L. According to the pumping le
CSCE 4115/5400 ASSIGNMENT #4
Due Wednesday, October 22, 2014
1. Consider a context-free grammar with the following productions:
S ASB |
A aAS | a
B SBS | A | bb
Give an equivalent context-free grammar with no useless symbols.
2. Put the following grammar
CSCE 4115/5400 AUTOMATA THEORY
TOPICS TO BE COVERED ON EXAM #2
November 4, 2013
The exam will cover everything we have discussed from Chapters 5-8 (Sections 5.4.4-7.5, 8.28.5.2) in the text and all presented materials, but emphasizing the material covered
ASSIGNMENT #2
Due Monday, September 15, 2014
1. Design deterministic nite automata to recognize the languages below. Test your DFAs using
Prolog on the indicated strings in the language, as well as some strings which are not in the
language.
(a) L = cfw_w
CSCE 4115/5400 ASSIGNMENT #4 SOLUTION
1. Consider a context-free grammar with the following productions:
S ASB |
A aAS | a
B SBS | A | bb
Give an equivalent context-free grammar with no useless symbols.
Since all symbols are accessible from S and all non
CSCE 4115/5400 ASSIGNMENT #2 SOLUTION
1. Design deterministic nite automata to recognize the languages below. Test your DFAs using
Prolog on the indicated strings in the language, as well as some strings which are not in the
language.
(a) L = cfw_w | w is
CSCE 4115/5400 EXAM #2 SAMPLE QUESTIONS SOLUTION
1. A context-free grammar where every production is either of the form A BC or A a is
said to be in Chomsky Normal Form.
2. True or False. The class of languages accepted by nondeterministic Turing machines
CSCE 4115/5400 ASSIGNMENT #3
Due Wednesday, October 30, 2013
1
1. Consider a context-free grammar with the following productions:
S AB | CA
Aa
B BC | AB
C aB | b
Give an equivalent context-free grammar with no useless symbols.
2. Put the following grammar
CSCE 4115/5400 ASSIGNMENT #2
Due Monday, September 30, 2013
1. Design deterministic finite automata to recognize the languages below. Test your DFA's using
Prolog on the indicated strings in the language, as well as some strings which are not in the
langu
CSCE 4115/5400 ASSIGNMENT #3 SOLUTION
1. Consider a context-free grammar with the following productions:
S AB | CA
Aa
B BC | AB
C aB | b
Give an equivalent context-free grammar with no useless symbols.
S CA
Aa
Cb
2. Put the following grammar into Chomsky
Chapter 4 Topics
Decision Properties of Regular Languages
Proving Languages Not to Be Regular
Equivalence and Minimization of Finite
Automata
Closure Properties of Regular Languages
Copyright 2013 Barrett R. Bryant. All rights reserved.
4-1
Properties
Chapter 9 Topics
Closure Properties of Recursive and
Recursively Enumerable Languages
Encodings of Problems
Diagonalization
The Universal Language
Undecidable Problems
Posts Correspondence Problem
Copyright 2013 Barrett R. Bryant. All rights reserve
Chapter 2 Topics
Deterministic Finite Automata
Nondeterministic Finite Automata
Finite Automata with -Transitions
Copyright 2013 Barrett R. Bryant. All rights reserved.
2-1
Deterministic Finite Automata
A formalism for defining languages,
consisting o
Chapter 8 Topics
Turing Machines
Programming Turing Machines
Extensions to the Basic Turing Machine
Restricted Turing Machines
Turing Machines and Computers
Copyright 2013 Barrett R. Bryant. All rights reserved.
8-1
Turing Machine Theory
In 1936, Alan Tu
Chapter 10 Topics
Classes P and NP
NP-Completeness of Satisfiability
Restricted Satisfiability
Additional NP-Complete Problems
Copyright 2013 Barrett R. Bryant. All rights reserved.
10-1
Time-Bounded TMs
A Turing machine that, given an input of
length n,
Chapter 3 Topics
Regular Expressions
Equivalence to Finite Automata
Copyright 2013 Barrett R. Bryant. All rights reserved.
3-1
REs: Introduction
Regular expressions are an algebraic way
to describe languages.
They describe exactly the regular
language
CSCE 4115/5400 ASSIGNMENT #4
Due Wednesday, December 4, 2013
1
1. Design Turing machines to recognize the following languages. You should use as many tapes
as necessary to simplify the design but the Turing machine must be deterministic and must
halt for
CSCE 4115/5400 AUTOMATA THEORY
TOPICS TO BE COVERED ON EXAM #1
October 2, 2013
The exam will cover everything we have discussed from Chapters 1-5 in the text and all presented materials, but emphasizing the material covered in class (e.g., very little of
CSCE 4115/5400 EXAM #1 SAMPLE QUESTIONS SOLUTION
1. The alphabet of a language is called a(n) set of terminal symbols when used in a grammar.
2. True or False. The following grammar is ambiguous.
S aSbS | bSaS |
True. S => aSbS => abS => abaSbS => ababS =
CSCE 4115/5400 EXAM #3 SAMPLE QUESTIONS SOLUTION
1. A(n) reduction is a translation of an instance of one problem P into an instance of another
problem P such that the solution of P implies a solution to P.
2. True or False. It is known that P NP but it c
CSCE 4115 ASSIGNMENT #1 SOLUTION
Fill in the Blank.
1. Name:
2. I have satisfied the prerequisites of CSCE 2100 Computing Foundations I and CSCE 2110
Computing Foundations II, or equivalents, with a grade of C or better in each.
Signature:
True or False.
CSCE 4115/5400 AUTOMATA THEORY
TOPICS TO BE COVERED ON EXAM #3
December 9, 2013
The exam will cover everything we have discussed from Chapters 8-10 (only section 8.6 was
covered in Chapter 8 but the entirety of Chapters 9 and 10 were covered) in the text
CSCE 4115/5400 AUTOMATA THEORY
TOPICS TO BE COVERED ON EXAM #2
November 4, 2013
The exam will cover everything we have discussed from Chapters 5-8 (Sections 5.4.4-7.5, 8.28.5.2) in the text and all presented materials, but emphasizing the material covered
CSCE 4115/5400 ASSIGNMENT #1
Due Wednesday, August 28, 2013, 2:50 P. M.
Fill in the Blank.
1. Name:
2. I have satised the prerequisite of CSCE 2100 Computing Foundations II, or equivalent, with
a grade of C or better.
Signature:
True or False.
For each of
Chapter 6 Topics
Pushdown Automata
Equivalence of Context-Free Grammars
and Pushdown Automata
Deterministic Pushdown Automata
Copyright 2013 Barrett R. Bryant. All rights reserved.
6-1
Pushdown Automata
The PDA is an automaton equivalent to the
CFG in
Chapter 7 Topics
Normal Forms for Context-Free Grammars
Proving Languages Not to Be Context-Free
Decision Properties of Context-Free
Languages
Closure Properties of Context-Free
Languages
Copyright 2013 Barrett R. Bryant. All rights reserved.
7-1
Vari
Chapter 1 Topics
Basic Definitions
Why Study Automata Theory?
Central Concepts of Automata Theory
Copyright 2013 Barrett R. Bryant. All rights reserved.
3-1
Languages
A language is a set of strings.
Everything in computer science is a
language
Set o
CSCE 4115 ASSIGNMENT #3
Due Monday, October 3, 2016
1. Find the minimum state finite automaton for the language specified by the deterministic finite
automaton given as a solution to Assignment #2, problem 3.
The DFA is M=(cfw_p0 , p1 , p2 , p3 , p4 , p5